The angles with a common reference angle of 18° in each quadrant will be 18° in the first quadrant, 162° in the second quadrant, 198° in the third quadrant, and 342° in the fourth quadrant.
Given that:
Interval of angle, 0° ≤ θ < 360°
Now we can use the reference angle to find an angle in each quadrant:
For the first quadrant, the angle θ is calculated as,
θ = 162° - 180° = 18°
For the second quadrant, the angle θ is calculated as,
θ = 180° - 18° = 162°
For the third quadrant, the angle θ is calculated as,
θ = 180° + 18° = 198°
For the fourth quadrant, the angle θ is calculated as,
θ = 360° - 18° = 342°
Therefore, the angles with a common reference angle of 18° in each quadrant are:
18° in the first quadrant162° in the second quadrant198° in the third quadrant342° in the fourth quadrantMore about the angled link is given below.
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Jensine earns $6 per hour babysitting,
She is saving to buy an MP3 player
that costs $150, but she does not yet
have enough money. If h represents
the number of hours she has spent
babysitting, which inequality describes
her situation?
507
Answer:
well maybe if Jensine gets a better f ***** job she can buy it instead she wants to waste her time to watch a annoying a *baby for 6$ a hour
Step-by-step explanation:
This is all a joke dont get mad :)
What is the approximate circumference of a circle that has a diameter of 379? Use 3.14 for π and express your answer to the hundredths place.
fill in the blank
__
thank you
The circumference of a circle with diameter 379 can be found using the formula:
C = πd
where d is the diameter of the circle. Substituting the given value of d, we get:
C = 3.14 x 379
C ≈ 1191.06
Rounding to the hundredths place, the circumference is approximately 1191.06 units of length (e.g. inches, centimeters, etc.).
Therefore, the answer to fill in the blank is 1191.06.
The star basketball player at your high school claims to make 50% of his three-point shots. Recently, he missed 7 of his first 10 three-point shots. Is this a surprising result if the player’s claim is true? Assume that the player is, in fact, able to make 50% of his three-point shots.
We need to carry out a simulation using a die to estimate the probability that he would miss 7 or more of his first 10 three-point shots.
answers
✔ even = make; odd = miss
✔ 100 times
The star basketball player at your high school claims to make 50% of his three-point shots. Recently, he missed 7 of his first 10 three-point shots. Is this surprising for this player? Assume that the player is, in fact, able to make 50% of his three-point shots. We need to carry out a simulation to estimate the probability that he would miss 7 or more of his first 10 three-point shots.
Here are the results of 100 simulated trials. Which of the following answers the question of interest?
answer: Based on the 100 simulated trials, there is about an 18% chance of the player missing 7 of his first 10 three-point shots. This probability is not unusually low, so it is not unlikely.
The probability that the player would miss 7 or more shots is given as follows: 17%.
As the probability is greater than 5%, it would not be a surprise.
What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 10, p = 0.5.
Hence the probability of 7 or more misses is given as follows:
P(X >= 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
Using a calculator, with the given parameters, the probability is given as follows:
P(X >= 7) = 0.17 = 17%.
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(3.6*10^-5)/(1.8*10^2)
Answer:
2*10^-7
Step-by-step explanation:
3.6*10^-5 is the same thing as [tex]\frac{1}{3.6*10^5}[/tex]. So [tex]\frac{1}{3.6*10^5}*\frac{1}{1.8*10^2}[/tex] is equal to [tex]\frac{1}{2*10^7}[/tex]which is equal to [tex]2*10^-7[/tex]
which equation matches the graph shown?
The correct option is C, the quadratic equation in the graph is:
y = -2x² + 4x - 2
How to find the quadratic equation?Here we have a quadratic equation. We can see that the vertex is at (1, 0), then if we assume that the leading coefficient is a, we can write it as:
y = a*(x - 1)²2
Now we also can see that it passes through the poin (0, -2), then we can replace these values there to get:
-2 = a*(0 - 1)²
-2 = a
Then the quadratic equation is:
y = -2*(x - 1)²
y = -2*(x² - 2x + 1)
y = -2x² + 4x - 2
The correct option is C.
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amanda wants to create a scale drawing of a rectangular porch that is 5 feet by 12 feet. The scale drawing needs to be as large as possible and fit on a sheet of paper that is 6 inches by 6 inches
The dimensions of the porch and the size of the paper indicates;
The appropriate scale for the drawing is the option 1 inch to 2 feet
1 in. : 2 feet
What is a scale drawing?A scale drawing is a drawing which has been increased or reduced compared to the size of the original or initial drawing.
The dimensions of the rectangular porch = 5 feet by 12 feet
The size of the sheet of paper = 6 inches by 6 inches
The limiting size from the actual porch is the length of 12 feet
Therefore;
The ratio of the length of the corresponding size of the drawing to the size actual porch is therefore;
6 inches is equivalent to 12 feet, which indicates;
6/6 = 1 inch is equivalent to 12/6 = 2 feet
The ratio is therefore; 1 in. : 2 ftThe possible question, obtained from a similar question posted on the net is to select the appropriate scale of the drawing
The possible options are;
1 in. : 2 ft.
1 in. : 2.5 ft.
6 in. : 2.5 ft.
2.5 in. : 6 ft.
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Please help I’m not sure what to fill into the table
There is no improvement this week because the average this week (43.04) is less than the average last week 52
Finding the number of minutes to improveGiven that we have the table of values
When the table is completed, we have the following entries
f x fx
6 32.5 195
7 37.5 262.5
8 42.5 340
9 47.5 427.5
7 52.5 367.5
So, we have
Average = Sum of fx/Sum of f
This gives
Average = (195 + 262.5 + 340 + 427.5 + 367.5)/(6 + 7 + 8 + 9 + 7)
Evaluate
Average = 43.04
The average last week was 52 minutes
43.04 is less than 52
This means that there is no improvement this week
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Please help me with this math!!
Answer:
Step-by-step explanation:
Distance formula looks a little like pythagorean because that where it comes from
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
=[tex]\sqrt{(-1-(-2))^{2}+(3-1)^{2} }[/tex]
=[tex]\sqrt{1^{2}+2^{2} }[/tex]
=√5 or 2.24
in a university seminar, the ratio of the number of boys to girls is 8 : 5. if there are 160 girls, the total number of students in the seminar is?
The total number of students in the seminar is 258, with 98 boys and 160 girls given a ratio of 8:5 between boys and girls.
We can begin by using the given ratio of boys to girls, which is 8:5, and the information that there are 160 girls to find the number of boys in the seminar.
If the ratio of boys to girls is 8:5, then we can say that for every 8+5=13 students, there are 8 boys and 5 girls.
To find the number of boys, we can set up a proportion
8/13 = x/160
where x is the number of boys.
Simplifying this proportion, we get
x = 8/13 × 160
x = 98.46
Therefore, the number of boys in the seminar is approximately 98.
To find the total number of students in the seminar, we can add the number of boys and girls
Total number of students = Number of boys + Number of girls
Total number of students = 98 + 160
Total number of students = 258
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4. Allie orders candles from an online company that offers a flat rate for shipping. She placed an order for 4 candles
for $35. A few months later, she placed an order for 12 candles for $49.
a. Define your Variables
b. What information were you given?
c. Create an equation using the information you were given.
d. How much was the shopping?
e. How many candles can she get for $60?
a. Let x be the cost of each candle, and let s be the flat rate shipping fee.
b. Allie placed two orders: one for 4 candles at a cost of $35, and one for 12 candles at a cost of $49.
c. From the first order, we know that:
4x + s = 35
From the second order, we know that:
12x + s = 49
d. To find the shipping fee, we can subtract the cost of the candles from the total cost of each order. For the first order:
s = 35 - 4x
Substituting this into the second equation, we get:
12x + (35 - 4x) = 49
Simplifying and solving for x, we get:
8x = 14
x = 1.75
Substituting this value of x into the first equation to solve for s, we get:
4(1.75) + s = 35
s = 28 - 4(1.75) = 21
Therefore, the shipping fee was $21.
e. Let n be the number of candles she can get for $60. We can set up an equation based on the cost per candle:
nx + s = 60
Substituting the values we found for x and s, we get:
n(1.75) + 21 = 60
Solving for n, we get:
n = (60 - 21) / 1.75 = 22.29
Since Allie cannot buy a fraction of a candle, she can buy a maximum of 22 candles for $60.
for a group of objects made of the same material the weight of an object varies directly with its volume.If an object that has a volume of 30 cubic inches weighs 24 ouncess what is the constant of variation
If an object that has a volume of 30 cubic inches weighs 24 ouncess then the constant of variation is 0.8.
If the weight of an object varies directly with its volume, then we can write the following proportion
Weight / volume = constant of variation
Let's use w to represent the weight of the object and v to represent its volume. We are given that an object with a volume of 30 cubic inches weighs 24 ounces, so we can write
w / v = k
Where k is the constant of variation. We can solve for k by substituting the given values
24 / 30 = k
Simplifying this expression, we get
0.8 = k
Therefore, the constant of variation is 0.8.
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you may need to use the appropriate appendix table to answer this question. suppose that the mean daily viewing time of television is 8.35 hours. use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household (a) what is the probability that a household views television between 4 and 12 hours a day? (round your answer to four decimal places.) (b) how many hours of television viewing must a household have in order to be in the top 4% of all television viewing households? (round your answer to two decimal places.) hrs (c) what is the probability that a household views television more than 3 hours a day? (round your answer to four decimal places.)
(a) The probability that a household views television between 4 and 12 hours a day is 0.8864. (b) A household must view at least 12.63 hours of television/day to be in the top 4% of all television viewing households. (c) The probability that a household views television more than 3 hours a day is 0.9830.
(a) To find the probability that a household views television between 4 and 12 hours a day, we need to standardize the values using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
For x = 4 hours:
z = (4 - 8.35) / 2.5 = -1.74
For x = 12 hours:
z = (12 - 8.35) / 2.5 = 1.46
Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores:
P(z < -1.74) = 0.0401
P(z < 1.46) = 0.9265
Therefore, the probability that a household views television between 4 and 12 hours a day is:
P(4 ≤ x ≤ 12) = P(z < 1.46) - P(z < -1.74) = 0.9265 - 0.0401 = 0.8864 (rounded to four decimal places).
(b) To find the number of hours of television viewing a household must have in order to be in the top 4% of all television viewing households, we need to find the z-score that corresponds to the top 4% of the normal distribution:
P(z > z*) = 0.04
Using a standard normal distribution table or a calculator, we can find that the z-score that corresponds to a probability of 0.04 is approximately 1.75.
Using the formula for z-score:
z = (x - μ) / σ
We can solve for x:
x = μ + zσ = 8.35 + 1.752.5 = 12.63 (rounded to two decimal places)
Therefore, a household must view at least 12.63 hours of television per day to be in the top 4% of all television viewing households.
(c) To find the probability that a household views television more than 3 hours a day, we can standardize the value of x = 3 using the formula for z-score:
z = (x - μ) / σ = (3 - 8.35) / 2.5 = -2.14
Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score:
P(z > -2.14) = 0.9830 (rounded to four decimal places).
Therefore, the probability that a household views television more than 3 hours a day is 0.9830.
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 47, with a median of 16
Bus 14, with a median of 14
Bus 47, with a mean of 16
Bus 14, with a mean of 14
The best measure of center to determine which bus typically has the faster travel time is: A. Bus 47, with a median of 16.
What is a line plot?In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
For Bus 47, the median is given by;
4,6,14,28,10,10,12,12,18,18,22,22,16,16,16
Median of Bus 47 = 16
Mean of Bus 47 = 15.
For Bus 14, the median is given by;
10,16,20,28,8,8,14,14,18,18,18
Median of Bus 14 = 16.
Mean of Bus 14 = 16
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what is 3125 divided by 25
Answer:
125
Step-by-step explanation:
By using normal division method,
3125÷25 goes as 125
PLSSSS HELP IF YOU TURLY KNOW THISSSS
Answer
x = 2
multiplie the 2 on both sides
= 4+3x = 10
subtract the 4
= 3x = 6
divide by 3
= x = 2
(7, –16)
(8, 0)
(7, 5)
Is this relation a function
The given relation (7, –16) (8, 0) (7, 5) is not a function.
To determine if the given relation is a function, we need to check if each input (x-value) is associated with only one output (y-value).
If there exists an input value that is associated with multiple output values, then the relation is not a function.
Looking at the given relation, we have:
(7, –16)
(8, 0)
(7, 5)
We can see that the input value 7 is associated with two different output values (-16 and 5).
When a relation is a function, each input value is associated with only one output value. In other words, each x-value has only one corresponding y-value. In this case, we have an input value of 7 that is associated with two different output values, which violates the definition of a function.
Therefore, the given relation is not a function.
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About 10 years ago I could get a haircut for $7, nowadays it costs $20. The rate of inflation is % ( round answer to nearest whole number)
Answer:
11%
Step-by-step explanation:
You want to know the rate of inflation if the price of a haircut increased from $7 to $20 in 10 years.
InflationThe inflation of prices is modeled by an exponential function.
p(t) = p₀·(1 +r)^t
where p₀ in the price at t=0, r is the annual inflation rate, and t is the number of years.
Solving for r, we find ...
p(t)/p₀ = (1 +r)^t . . . . . . . . divide by p₀
(p(t)/p₀)^(1/t) = 1 +r . . . . . . take the t-th root
r = (p(t)/p₀)^(1/t) -1 . . . . . . . subtract 1
For the given numbers, we find the rate to be ...
r = (20/7)^(1/10) -1 ≈ 0.11 = 11%
The rate of inflation is 11% per year.
<95141404393>
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru is able to estimate their wait time more consistently, and why?
Fast Chicken, because it has a smaller IQR
Fast Chicken, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
From the given question we cannot conclude that Burger Quick has a smaller range based on the given information.
Range refers to the set of potential target value, and if we have a graph, then the range is the collection of all feasible y-values on the graph.
Burger Quick is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data, and a smaller IQR indicates that the data is more tightly clustered around the median. In this case, Burger Quick has an IQR of 14.5 (from 9.5 to 24), while Fast Chicken has an IQR of 4.5 (from 10 to 14.5). This means that the wait times reported by Burger Quick are more consistent and less variable than those reported by Fast Chicken.
The range is a measure of the total spread of the data, and while a smaller range can indicate less variability, it doesn't necessarily mean that the data is more consistent in the middle. Therefore, we cannot conclude that Burger Quick has a smaller range based on the given information.
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What fraction does the red dot represent on the number line above?
Answer:
The answer would be Option C. [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
If ha is not equals, you have to double the probability of being beyond your test statistic to get your p-value.a. Trueb. False
True. The statement "If Ha is not equal, you have to double the probability of being beyond your test statistic to get your p-value" is true.
If the alternative hypothesis (ha) is not equal, then you have to double the probability of being beyond your test statistic in order to obtain the p-value.
This is because the p-value represents the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. When ha is not equal, the probability of observing a test statistic as extreme in the opposite direction is also relevant for determining the significance of the result. Doubling the one-sided probability accounts for both possibilities and provides a more accurate estimate of the significance level.Thus, When the alternative hypothesis (Ha) is not equal (two-tailed test), you need to consider both tails of the distribution, so you double the probability of being beyond the test statistic to calculate the p-value.
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Please help me with this homework
Answer:
Area = 35 cm².Step-by-step explanation:
We are given with a triangle whose Height is 7 cm and base is 10 cm.
We have to calculate the Area of triangle.
As we know that area of triangle is calculated by,
Area = ½ × base × heightPutting the required values we get,
Area = 1/2 × 7 × 10
Area = 7 × 5
Area = 35 cm².
Hence, The area of the triangle is 35 cm².
Complete the table.
(Type an integer or a simplified fraction.)
please help, no links
The complete table is as follows
x y
0 -11/2
1 -3
2 -1/2
3 2
4 9/2
5 7
How to complete the tableThe table is completed by identifying the constant change
-11/2 + k = -3
k = -3 + 11/2
k = 5/2
This is used to complete the table as follows
For x = 1
-11/2 + 5/2 = -3
For x = 2
-3 + 5/2 = -1/2
For x = 3
-1/2 + 5/2 = 2
For x = 4
2 + 5/2 = 9/2
For x = 5
9/2 + 5/2 = 7
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where g(x) is the translation 1 unit down of f(x)=x2.
The required equation of function g(x) is x²- 1.
To find the function g(x), which is the translation 1 unit down of f(x) = x², we can subtract 1 from the y-coordinate of each point on the graph of f(x).
The graph of f(x) = x² is a parabola that opens upward and passes through the origin (0, 0). The y-coordinate of any point on this parabola is equal to the square of its x-coordinate.
The function g(x) can be written as:
g(x) = f(x) - 1
= x² - 1
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After the translation 1 unit down of the function f(x)=x² is g(x) = x² - 1.
The given function is f(x)=x².
The translation of a function f(x) 1 unit down is given by g(x) = f(x) - 1.
So, for f(x) = x², the translation 1 unit down of f(x) is g(x) = x² - 1.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: None
Vertical Shift: Down 1 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
Therefore, after the translation 1 unit down of the function f(x)=x² is g(x) = x² - 1.
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Determine whether the function y=9x represents exponential growth or exponential decay. Then graph the function.
It represents exponentially growth function.
The given function is
y = [tex]9^{x}[/tex]
Since,
A mathematical function with the form f (x) = [tex]a^{x}[/tex] is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be greater than 0.
Now after plotting,
It begins as a horizontal line, grows slowly at first, then picks up speed. It has an increasing slope.
Which represents exponentially growth.
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Mrs Mojapelo cooks chicken pieces and puts the dish in the f The freezer lowers the temperature from 15 °C to -18 °C. What is the temperature range?
The temperature range is the difference between the highest and lowest temperatures. To calculate it, we subtract the lowest temperature from the highest temperature. In this case, we have:
**Temperature range = 15 °C - (-18 °C) = 15 °C + 18 °C = 33 °C**
So, the temperature range is **33 °C**.️
managers should never make decisions unless they have enough data to make a perfect statistical decision based on sufficient values for the mean, standard deviation, and sample size. managers should never make decisions unless they have enough data to make a perfect statistical decision based on sufficient values for the mean, standard deviation, and sample size. true. managers who fail to account for all possible data, even if a decision must be delayed, will always make an inferior decision. true. managers who take the time to consult with their staff and key sources of evidence will never arrive at an inferior decision. false. managers can usually just have a mean difference and make a judgment call that is right at a 95% confidence interval. false. although math and data can help make decisions clearer, eventually we always just have to make a judgment call.
Mathematics and data can help make decisions clearer, but ultimately you only have to make one decision at a time. This statement is true.
Information and factual investigation give profitable bits of knowledge and back decision-making, but it isn't continuously conceivable or fundamental to have full factual information sometime recently making decisions.
Decisions often have to be made with fragmented or fragmented data, and managers use them to possess judgment and encounter to weigh accessible alternatives, and make the most excellent conceivable choices.
A decision must be made. Additionally, decisions often involve more than purely numeric data, such as B.
Social and ethical considerations require thoughtful and nuanced decisions that are not always fully captured by statistical analysis.
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Here is a map of an island
with cities A, B and C.
Jeremy drives from A to B on
the route shown.
Kia drives from B to C on
the route shown.
C
B
Work out how much further Jeremy drives than Kia.
You must show your working.
Show your working
+
Answer:
km
A
Scale: 1 cm represents 200 km
The distance further than Kia, that Jeremy had to drive can be found to be 100 kilometers.
How to find the distance traveled ?Assuming that the picture posted is up to scale, we can use a ruler to find the distance that Jeremy drives from A to B to be 5 centimeters. This means that the actual distance is :
= 5 x 200 per cm
= 1, 000 kilometers
Using that same ruler, we can find that Kia drove 4. 5 cm from B to C which means the actual distance was :
= 4. 5 x 200
= 950 kilometers
The distance more than Kia that Jeremy drove was:
= 1, 000 - 900
= 100 kilometers
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IF 4 dice are thrown, what is the probability of getting
i.exactly 3sixes
ii.exactly2sixes
iii.no sixes.
When rolling a fair six-sided die, the probability of rolling a six is 1/6. Assuming that the dice are fair and independent, we can use the rules of probability to find the probability of rolling certain outcomes when 4 dice are thrown:
i. To find the probability of getting exactly 3 sixes when 4 dice are thrown, we can use the binomial probability formula:
P(exactly k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.
For this problem, n = 4, k = 3, and p = 1/6.
P(exactly 3 sixes) = (4 choose 3) * (1/6)^3 * (5/6)^1
= 4 * (1/216) * (5/6)
= 5/54
Therefore, the probability of getting exactly 3 sixes when 4 dice are thrown is 5/54.
ii. To find the probability of getting exactly 2 sixes when 4 dice are thrown, we can use the same formula with k = 2:
P(exactly 2 sixes) = (4 choose 2) * (1/6)^2 * (5/6)^2
= 6 * (1/36) * (25/36)
= 25/72
Therefore, the probability of getting exactly 2 sixes when 4 dice are thrown is 25/72.
iii. To find the probability of getting no sixes when 4 dice are thrown, we can use the complement rule:
P(no sixes) = 1 - P(at least one six)
To find the probability of getting at least one six, we can use the complement of getting no sixes:
P(at least one six) = 1 - P(no sixes)
For each die, the probability of not rolling a six is 5/6. Therefore, the probability of getting no sixes on 4 dice is:
P(no sixes) = (5/6)^4
= 625/1296
Therefore, the probability of getting no sixes when 4 dice are thrown is 625/1296, and the probability of getting at least one six is 1 - 625/1296 = 671/1296.
List the sample space for rolling a fair eight-sided die.
S = {1}
S = {8}
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8}
The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}.
The sample space is the set having the total outcomes of a random trial.
So, in a fair eight-sided die, the outcomes will be =
1, 2, 3, 4, 5, 6, 7, 8 = 8
Writing in the of set, S = {1, 2, 3, 4, 5, 6, 7, 8}.
Hence the sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}.
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The value of a computer that originally sold for $800 can be modeled by g(x)=800(0.8^x), where x is the number of years since the computer was purchased. Describe g(x) as a translation of the parent function f(x)=0.8^x.
Answer:
Step-by-step explanation:
The parent function is f(x) = 0.8^x, which represents exponential decay. This means that as x increases, f(x) gets smaller and smaller.
The given function g(x) is obtained by multiplying f(x) by 800, which stretches the graph vertically by a factor of 800.
Also, the function g(x) has an additional translation: the entire graph of f(x) is shifted vertically upwards by 800 units. This is because the computer originally sold for $800, and g(x) represents the current value of the computer, which is $800 times the value of the parent function.
Therefore, g(x) can be described as a vertical stretch and translation of the parent function f(x) = 0.8^x.
